In a conventional wireless communication system, it is important to have a strong communication signal. In particular, the greatest possible signal-to-noise ratio (SNR) is desired at a receiver end. Similarly, for a Wi-Fi system, increasing the SNR at the receiving device increases the probability that frames are correctly received and reduces the amount of retransmissions necessary from the source. Some methods of achieving better SNR at the receiver end is to increase transmit power, decrease the distance between the source and the receiver, and increase antenna gain.
In Wi-Fi, non-compressed beamforming and compressed beamforming may be used. Compressed beamforming reduces the amount of feedback. In addition, Wi-Fi introduced group feedback, i.e., feedback only once in an Ng group of subcarriers, where Ng represents a number of subcarriers in a subcarrier group. In long term evolution/new radio (LTE/NR), two step beamforming is used to reduce overhead, where one matrix is used with wideband and another matrix is used with a subband.
In a conventional Wi-Fi system, beamforming increases antenna gain while maintaining omnidirectional coverage, which results in increased SNR and more stable, higher bandwidth Wi-Fi connections by focusing transmissions to the recipient. These benefits are achieved by transmitting a signal via an array of antennas and slightly altering the phase of the signal at each antenna in the array. For example, the Institute of Electrical and Electronics Engineers (IEEE) 802.11 ac standard (i.e., a wireless networking standard in the 802.11 family, developed by the IEEE Standards Association) provides a protocol for calibrating an array of antennas to direct a signal to any point covered under omnidirectional propagation. A beamformer is a device that augments the phase shift of antennas to produce a gain in a desired direction. A beamformee is a device that is a target of a beamformer. The beamformee participates in the establishment of the beam, but does not augment timings of its antennas.
In the IEEE 802.11 ac standard, a compressed beamforming report is generated per user, based on a singular value decomposition (SVD) of the channel. After obtaining a beamforming matrix, the beamforming matrix is compressed using multiplications of diagonal matrices and Givens rotation matrices, where H(k) is an Nr×Nt channel matrix on a subcarrier k, Nr is a number of receive antennas, and Nt is a number of transmit antennas. The channel matrix is first estimated at the receiver by frequency domain channel estimation based on a received long training field (LTF). SVD is then applied on the estimated channel matrix, which results in Equation (1) as follows:H(k)=U(k)·S(k)·V′(k)  (1)where S(k) is a diagonal singular value matrix containing singular values in a decreasing order on the diagonal of the singular value matrix, U(k) is a left singular matrix containing left singular vectors in corresponding order, and V(k) is a right singular matrix containing right singular vectors in the same order. The matrix V(k) of size Nr×Nt is semi-unitary.
SVD-based single user beamforming in the IEEE 802.11 ac standard requires that the right singular matrix be decomposed, quantized, and then fed back to the transmitter for efficient transmit beamforming. The matrix V may be decomposed in Equation (2) as follows:V=[Πi=1min(Nc,Nr−1)[Di(1i-1ejϕi,i . . . ejϕNr−1,i1)Πl=i+1NrGliT(Ψli)]]ĨNr×Nc  (2)
Conventional Wi-Fi feedback provides quantization for each subcarrier, which results in a large increase in the amount of feedback as the number of antennas increases. Next generation Wi-Fi will have a large number of antennas. Thus, the amount of feedback will increase significantly if a conventional feedback mechanism is used.